An electromagnetic flowmeter is used to measure blood flow rates during surgery. Blood containing Na" ions flows due south through an artery with a diameter of $0.40 \mathrm{cm} .$ The artery is in a downward magnetic field of $0.25 \mathrm{T}$ and develops a Hall voltage of $0.35 \mathrm{mV}$ across its diameter. (a) What is the blood specd (in $\mathrm{m} / \mathrm{s}$ )? (b) What is the flow rate (in $\mathrm{m}^{3} / \mathrm{s}$ )? (c) The leads of a voltmeter are attached to diametrically opposed points on the artery to measure the Hall voltage. Which of the two leads is at the higher potential?
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Step 1
35 \, \text{mV} = 0.35 \times 10^{-3} \, \text{V}\) - Diameter of the artery, \(w = 0.4 \, \text{cm} = 0.004 \, \text{m}\) - Magnetic field, \(B = 0.25 \, \text{T}\) Substitute the values into the formula to find the blood speed. ** Show more…
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An electromagnetic flowmeter is used to measure blood flow rates during surgery. Blood containing $\mathrm{Na}^{+}$ ions flows due south through an artery with a diameter of $0.40 \mathrm{cm} .$ The artery is in a downward magnetic field of $0.25 \mathrm{T}$ and develops a Hall voltage of $0.35 \mathrm{mV}$ across its diameter. (a) What is the blood speed (in $\mathrm{m} / \mathrm{s}) ?$ (b) What is the flow rate (in $\mathrm{m}^{3} / \mathrm{s}$ )? (c) The leads of a voltmeter are attached to diametrically opposed points on the artery to measure the Hall voltage. Which of the two leads is at the higher potential?
An electromagnetic flowmeter is used to measure blood flow rates during surgery. Blood containing ions (primarily $\mathrm{Na}^{+}$ ) flows through an artery with a diameter of $0.50 \mathrm{~cm}$. The artery is in a magnetic field of $0.35 \mathrm{~T}$ and develops a Hall voltage of $0.60 \mathrm{mV}$ across its diameter. (a) What is the blood speed (in $\mathrm{m} / \mathrm{s}$ )? (b) What is the flow rate $\left(\mathrm{in} \mathrm{m}^{3} / \mathrm{s}\right) ?(\mathrm{c})$ If the magnetic field points west and the blood flow is north, is the top or bottom of the artery at the higher potential?
(II) The Hall effect can be used to measure blood flow rate because the blood contains ions that constitute an electric current. $(a)$ Does the sign of the ions influence the emf? (b) Determine the flow velocity in an artery 3.3 $\mathrm{mm}$ in diameter if the measured emf is 0.13 $\mathrm{mV}$ and $B$ is 0.070 $\mathrm{T}$ . (In actual practice, an alternating magnetic field is used.)
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